Abstract: The present invention relates to a system for using signals scattered by targets to determine position and velocity for each of the targets and comprises a set of transmitters and receivers of electromagnetic or acoustic signals, said transmitters and receivers dispersed to known points. Each pair of transmitter and receiver, monostatic or bistatic, is named a measuring facility. The ranges of the transmitters are chosen so that a target at an arbitrary point within the position space can be measured via scattering in the target by at least four measuring facilities. For each measuring facility, target detection occurs with constant false alarm rate in the form of probabilities over resolution cells with regards to range and Doppler velocity and conceivable targets are placed in a 2-dimensional linear space belonging to the measuring facility.

Abstract: A method and apparatus for dimensioning and, optionally, weighing a cuboidal object. Four distance sensors are employed, one downwardly facing the top of the object, one facing one side thereof and two respectively facing mutually parallel sides of the object perpendicular to the one side. Distances are measured between the sensors and the top and sides of the object and subtracted from known distances to determine the length, width, height and spatial volume of the object. The object may be weighed as it is being dimensioned. Spatial volume and a “dim weight” for the object may be calculated.

Abstract: The invention is a portable human height measuring device. The device consists of an ultrasonic distance sensor, a controller and several output units. The ultrasonic distance sensor measures a person's height. The control unit converts the electronic signals from the ultrasonic sensor to proper measuring standards. The measurement output units displays, announces, or/and prints the measurement. The device is integrated onto a baseball like cap. The ultrasonic sensor is mounted on the sun visor of the cap. The control and output units are mounted on the crown of the cap. A switch is mounted on the top of the inner cap. When the head of the person wearing the cap touches the switch, it triggers the ultrasonic sensor to start measuring. The person's height is then converted to the proper measuring unit, and communicated to the person via output units.

Abstract: The selection of multiple, suitably designed, demodulation reference signals can enable the measurement of a vehicle's speed using continuously transmitted frequency modulated (CTFM) signals. The unique solution of vehicle speed can be used to resolve the range Doppler ambiguity found in conventional CTFM sonar and radar systems. This can enable continuous range and speed estimates of high-speed vehicles with an attendant reduction in transmit power relative to pulse-echo systems with similar measures of performance due to the 100% duty cycle.

Abstract: An acoustic method for measuring of a distance between an emitter of acoustic energy and a target object provides for an accurate measurement by having the measurement's outcome invariant to the speed of sound variations along the acoustical path between the emitter and the target. A plurality of emitters and a plurality of receivers are used in the invention. One acoustic emitter and one receiver are located in a spatial region such that the sent and the reflected acoustical energy passes along substantially same vertical line between the emitter and the target. Another acoustic emitter sends the acoustical energy at an angled direction to the same area on the target's reflecting surface as the first emitter does. The corresponding echo travels to another receiver. During the measurement, two specific variables are being monitored such that possible variations of the speed of sound are irrelevant to the result of the distance measurement.

Abstract: A rear collision warning system (10) for a target vehicle (17) and an approaching vehicle (18) is provided. The rear collision warning system (10) includes a first transmitter (54) located on the approaching vehicle (18) and directed at the target vehicle (17). The first transmitter (54) generates a vehicle information signal. A first indicator (16) located on the target vehicle (17). A first receiver (50) electrically coupled to the first indicator (16) receives the vehicle information signal and transmits a warning signal to the approaching vehicle (18) when the vehicle information signal is above a predetermined magnitude. A method of performing the same is also provided.

Abstract: Arrangement with an acoustic array with a sound velocity meter, suitable to be arranged under water. The acoustic array is able to receive acoustic signals from an underwater device and to provide acoustic array output data to a processing arrangement such that the processing arrangement can perform in real-time, a calculation of a position of the underwater device relative to the acoustic array based on the acoustic array output data. The sound velocity meter is able to measure velocity of sound in fluid layers just below a vessel floating on the water and to provide sound velocity meter output data to the processing arrangement such that the processing arrangement can correct the calculation of the position of the underwater device based on the sound velocity meter output data in real-time.

Abstract: A method for processing echoes in a time-of-flight ranging system or level measurement system. The method comprises an initial noise floor level and identifying potential echoes in an echo signal above the initial noise floor level and a noise signal below the initial noise floor level. One or more portions of the initial noise floor level are modified and an adjusted noise floor level is generated by applying a cubic spline algorithm to the modified portions and the initial noise floor level. The adjusted noise floor level is then used to identify valid echoes in the echo signal and generate an echo signal profile.

Abstract: A device for detecting objects, especially used as a parking assistance device in a motor vehicle, includes a plurality of distance sensors, at least one microcontroller configured to control the distance sensors and an output unit. The distance sensors emit a signal in accordance with an identifier that is modified over time by the microcontroller.

Abstract: Proposed is a method for measuring distance, which improves the resolution and the selectivity in an echo method, using propagation-time measurement. In this context, a received signal is sampled without first having to smooth the signal.

Abstract: An improved transducer for a proximity sensing system using a sonar transmitter is disclosed. An autonomous device provided with a number of motor-driven wheels further comprises a number of elements for the proximity navigation and guiding of the device such as a microprocessor system and a proximity ultrasonic sensing system comprising at least one transmitting member and one receiving member. The transmitting member is formed by the ultrasound transducer (11), which is positioned behind a wire mesh at the front of the device. The device transmits ultrasonic waves from a first strip-shaped device (21) with a narrow vertical distribution within a wide horizontal sector, and a second strip-shaped device (22) providing a wider vertical distribution within a similarly wide horizontal sector in front of the autonomous device.

Abstract: The Biomimetic Sonar invention ensonifies submerged objects, digitizes acoustic images reflected from the ensonified objects, and classifies and stores the digitized images using electronic processing derived from that believed to be used by Tursiops truncatus, the bottlenose dolphin. The invention also provides a probable identification of an ensonified object based on comparison of an ensonified object with templates in a library of acoustic images.

Abstract: A method and system for high-pass filtering to remove DC and/or low frequency components of a receive signal from the transducer of a level measurement system. In one embodiment, the method includes generating a maximum signal profile and a minimum signal profile for the receive signal, generating a midpoint reference signal from the maximum and minimum signal profiles and subtracting the midpoint reference signal from the receive signal to produce a filtered signal.

Abstract: A method and system for echo processing a receive signal using autocorrelation. A receive signal is sampled, digitized and high-pass filtered. A correlation signal is created by adding the filtered signal to a copy of the filtered signal shifted by a time unit. A set of correlation signals is created by repeating the process for a range of time units corresponding to a set of sequential sample points. Each correlation signal has a correlation indicator evidencing the strength of the correlation. The correlation signal having the highest correlation strength is identified, and the time shift used to create it is identified as the time of flight of the echo pulse. The echo distance is then calculated based upon the time of flight and the speed of propagation of the echo in the environment. The correlation indicator may the maximum peak value of the correlation signal.

Abstract: A portable fish finder device with a housing that defines a wrap cavity for receiving a signal cable that communicates between a depth finder device and a transducer attached to the water craft. A skirt connected to the housing moves between a first position covering the wrap cavity and a second position uncovering the cavity for winding or unwinding the signal cable. The depth finder device pivotally mounts to the housing to move between a storage position with a display screen received in a recess of the housing and an extended position for viewing the display. The cable winds into the wrap cavity for storage and unwinds when the housing is disposed on a portion of a water craft for use of the depth finder with the transducer communicating signals in a body of water for detecting underwater articles.

Abstract: A patient monitoring system can be used in multiple locations to monitor a patient using distinct monitoring strategies. For instance, the same system can be used both on a chair and on a bed. When a base unit of the system is attached to a chair to monitor an area or volume in the vicinity of the chair, it is typically set to sound an alarm when a transmitted signal takes too long to be reflected back to the base unit, indicating that the patient has moved beyond the proper range for sitting. The system also features remote unit(s) and module(s) that can be attached to the base unit, directly or indirectly, to facilitate perimeter monitoring when a patient is lying in a bed. In this case, the system is typically set to sound an alarm when a transmitted signal is interrupted by the patient and reflected back, indicating that the patient may have attempted to get out of bed.

Abstract: A distance sensor device, in particular as a component of a parking aid or reversing aid for a motor vehicle, includes one or more distance sensors and a distance sensor control device for the purpose of activating the distance sensor or sensors via a respective signal line using an activation pulse that is quasi-digital and time-analog. At least one of the distance sensors has two different modes of operation. The modes of operation may be switched by varying the duration and/or amplitude of the activation from the distance sensor control device.

Abstract: A method and apparatus for dimensioning and, optionally, weighing a cuboidal object. Four distance sensors are employed, one downwardly facing the top of the object, one facing one side thereof and two respectively facing mutually parallel sides of the object perpendicular to the one side. Distances are measured between the sensors and the top and sides of the object, and subtracted from known distances to determine the length, width, height and spatial volume of the object. The object may be weighed as it is being dimensioned. Spatial volume and a “dim weight” for the object may be calculated.

Abstract: A calibration module and methods for a time-of-flight ranging system. The calibration module may be built into the circuitry of the time-of-flight ranging system and allows various operating parameters to be measured and evaluated. The calibration modes include amplitude calibration, frequency calibration, and time delay calibration. The calibration mode also includes an electronic noise measurement mode. The calibration modes may be initiated on power-up or reset, or in response to user input or time-based trigger.

Abstract: An airborne sonar collision avoidance system is disclosed. The system compensates for changes in temperature in real time to provide more accurate sonar detection. In addition, the sensors are arranged in a communications network that allows for the sensors to be programmed at run time, thus providing the ability to relocate the sensors without having to pre-program the sensors before the sensors are installed onto a different location.

Abstract: The relative position and orientation between two subsea structures (210, 212) are measured by ultra-short baseline acoustic metrology. Dual mode master/slave (220, 222) stations comprising a multi-transducer array are fitted in known position and orientation relative to each structure. The first station (220) is operated in master mode to determine the position and direction of the second structure (222) relative to the first (220). The second station (222) is operated in master mode to determine the position and direction data from both operations the apparatus calculates relative position and orientation between the structures. The dual mode stations can be replaced by a master station and a slave station, swapping places.

Abstract: A buoy to shore fish finding system has a buoyant station with a sonar transmitter, a sonar receiver, a sonar to electric signal transducer and a radio transmitter all controlled by a microprocessor. The system shore station has a radio receiver and signal display controlled by a shore station microprocessor. The buoyant station microprocessor is programmed to generate sync pulses and to transmit both the sync pulses and transduced sonar echo returns to the shore station while the shore station microprocessor is programmed to display only echo signals received after a sync pulse. The shore station is detachably secured to the arm of the fisherman or to his fishing rod.

Abstract: A vehicle object detection system is disclosed that audibly conveys to the vehicle operator the direction of the detected object relative to the vehicle through the vehicle's audio system. The system includes a sensor array, a processor, and a speaker arrangement. The sensor array detects an object remote from the vehicle and generates a signal when an object has been detected. The processor receives and processes the sensor array signal. Then, the processor transmits the processed signal to the speaker arrangement. The speaker arrangement audibly conveys the processed signal over multiple audio channels. The method of detecting an object remote from the vehicle is also disclosed.

Abstract: An acoustic method for measuring of a distance between an emitter of acoustic energy and a target object provides for an accurate measurement by having the measurement's outcome invariant to the speed of sound variations along the acoustical path between the emitter and the target. A plurality of emitters and a plurality of receivers are used in the invention. One acoustic emitter and one receiver are located in a spatial region such that the sent and the reflected acoustical energy passes along substantially same vertical line between the emitter and the target. Another acoustic emitter sends the acoustical energy at an angled direction to the same area on the target's reflecting surface as the first emitter does. The corresponding echo travels to another receiver. During the measurement, two specific variables are being monitored. The first variable is associated with the distance between the first emitter and the target.

Abstract: A pulse offset calibration method for a pulse-echo level measurement system. The pulse-echo level measurement system includes a transducer for transmitting calibration acoustic pulses and receiving echo pulses. A receiver converts the echo pulses into corresponding pulse profile signals having a leading edge. A static delay interval is defined on the leading edge corresponding to the time interval between the reception of the echo pulse and the response by the receiver. A dynamic delay interval is defined on the leading edge corresponding to the time response characteristics of the transducer and the receiver. The static delay interval and the dynamic delay interval are summed to determine the offset time interval for the echo pulse. The offset time interval is subtracted from the measurements to provide the true duration for the time of flight.

Abstract: A buoy to shore fish finding system has a buoyant station having a sonar transmitter, a sonar receiver, a sonar to electric signal transducer and a radio transmitter all controlled by a microprocessor. A shore station has a radio receiver and signal display controlled by a shore station microprocessor. The buoyant station microprocessor is programmed to generate sync pulses and to transmit both the sync pulses and tranduced sonar echo returns to the shore station while the shore station microprocessor is programmed to display only echo signals received after a sync pulse.

Abstract: A distance measuring system includes a housing with at least one surface, at least one switch along the one surface of the housing, an energy system in the housing, and a distance computation system coupled to the energy system. The switch has an inactivated position and an activated position when pressed against an origination object. The activated position of the switch identifies the surface as a reference plane with respect to the origination object. The energy system transmits energy towards a target when the switch is in an activated position and receives at least a portion of the energy which is reflected back from the target. The distance computation system uses the received portion of the energy which is reflected back and the identification of the surface as the reference plane to determine a distance from the origination object to the target.

Abstract: A buoy to shore fish finding system has a buoyant station having a sonar transmitter, a sonar receiver, a sonar to electric signal transducer and a radio transmitter all controlled by a microprocessor. A shore station has a radio receiver and signal display controlled by a shore station microprocessor. The buoyant station microprocessor is programmed to generate sync pulses and to transmit both the sync pulses and tranduced sonar echo returns to the shore station while the shore station microprocessor is programmed to display only echo signals received after a sync pulse.

Abstract: A fishing system buoy has a watertight bulbous shell housing an electronic load and with a center of mass located within a lower half of the shell. The load includes sonar operatively coupled via a microprocessor with a radio transmitter that has an upright antenna located in an upper half of the shell. The shell has a keel with an eyelet for tethering a fishing line to the shell. The buoy functions both as a fishing bobber and communications relay station for obtaining and transmitting images of fish swimming beneath the bobber.

Abstract: A device for detecting objects, especially used as a parking assistance device in a motor vehicle, includes a plurality of distance sensors, at least one microcontroller configured to control the distance sensors and an output unit. The distance sensors emit a signal in accordance with an identifier that is modified over time by the microcontroller.

Abstract: An apparatus and method for detecting utilities buried in the ground wherein an array of sonic receivers are arranged in rows and ranks against the ground and a corresponding array of sonic transmitters are arranged relative to the array of sonic receivers so that a distance between each sonic transmitter and each adjacent sonic receiver is the same. Echoes generated by the apparatus may then be normalized, averaged and compared to the original echoes to develop a profile of the buried utility.

Abstract: A measuring system and method of detecting an object distance by transmission media with different wave velocities are described. The measuring system has a computer, a primary detector and a secondary detector. The primary detector is connected to the computer through bus communication and the secondary detector connected to the primary one through two different transmission media. The primary detector is able to receive separately a first signal and a second signal emitted simultaneously from the secondary detector through the transmission media. Moreover, the first signal has light-speed and the second signal has sound-speed. To calculate the distance between the objects which the primary and the secondary detector are attached respectively. The delay time of second signal and the wave velocity of the supersonic media are multiplied.

Abstract: A calibration module and methods for a time-of-flight ranging system. The calibration module may be built into the circuitry of the time-of-flight ranging system and allows various operating parameters to be measured and evaluated. The calibration modes include amplitude calibration, frequency calibration, and time delay calibration. The calibration mode also includes an electronic noise measurement mode. The calibration modes may be initiated on power-up or reset, or in response to user input or time-based trigger.

Abstract: The present inventions comprise a method of estimating a minimum range for a target with respect to a first point of interest, independent of actual, range to the target, comprising obtaining three bearing data points; using the three bearing data points to determine a speed contribution Vos of a first point of interest to a distance from a relative velocity vector over a time frame comprising t0 to t0′; determining an angle &thgr;&bgr; as defined by the bearing relative to ownship's heading at the point in time of closest approach to a second point of interest; and calculating a minimum range using a predetermined formula.

Abstract: A myocardial revascularization device has a catheter suitable for use in a myocardial revascularization procedure, the catheter including an elongate body having a proximal end and a distal end, and tissue-ablating means housed at least partially within the catheter and capable of effectuating tissue ablation adjacent the distal end of the catheter. The device further has an optical reflectance fiber housed within the catheter and coupled to an optical reflectance system. The device is operative to transmit a reflectance signal in the optical reflectance fiber, the reflectance signal including either short optical pulses or low-coherence light. The optical reflectance system is operative to gauge tissue ablation, measure a thickness of tissue adjacent the catheter, and/or determine a position of the distal end relative to adjacent tissue using either of optical time-domain reflectance or optical coherence interferometry.

Abstract: System and methods are disclosed for fluid measurements which may be utilized to determine mass flow rates such as instantaneous mass flow of a fluid stream. In a preferred embodiment, the present invention may be utilized to compare an input mass flow to an output mass flow of a drilling fluid circulation stream. In one embodiment, a fluid flow rate is determined by utilizing a microwave detector in combination with an acoustic sensor. The acoustic signal is utilized to eliminate 2&pgr; phase ambiguities in a reflected microwave signal. In another embodiment, a fluid flow rate may be determined by detecting a phase shift of an acoustic signal across two different predetermined transmission paths. A fluid density may be determined by detecting a calibrated phase shift of an acoustic signal through the fluid. In another embodiment, a second acoustic signal may be transmitted through the fluid to define a particular 2&pgr; phase range which defines the phase shift.

Abstract: A power saving system and method for the analog-to-digital converter stage in a time of flight ranging system. A receiving echo signal having an envelope is converted into a digital form suitable for further processing by sampling the received echo signal envelope at precise intervals to obtain amplitude measurement points. An interpolation function is applied between each pair of adjacent amplitude measurement points. The application of the interpolation function provides a closer approximation of the shape of the received echo signal envelope without the need to use higher sampling rates which means slower analog-to-digital converters may be utilized resulting in power and cost savings.

Abstract: A ground penetrating radar system including a processor for generating audible output signals having discrete frequency components representative of the depth of buried targets. The amplitude of the audible frequency components is representative of the size or mass of the target.

Abstract: A method of detecting actual or incipient submersion of an electroacoustic transducer (2) facing downwardly toward a surface of fluent material to be sensed in a pulse-echo acoustic ranging system, the transducer having a skirt (6) surrounding a downwardly facing radiating surface (4) to maintain an air space (10) beneath the radiating surface even under submergence conditions, and the transducer being electrically energized to emit pulses of acoustic energy from the radiating surface, the system processing an electrical output received from the transducer following a pulse by repeatedly sampling it to obtain a response profile. Samples from an initial portion of the response of the transducer during a ring-down period following the transmit pulse are summed (FIG.

Abstract: A device for non-contractual measurement of the speed of an object moving over a surface comprises a means for radiating a signal of fixed frequency at an angle onto the surface in or against the direction of motion, said angle being variable by the movement of the object, and for receiving a Doppler-shifted signal reflected at the surface. A means is provided for combining a plurality of reflected Doppler-shifted signals, which are received in temporal succession, so as to produce a combined spectrum. The device for non-contractual speed measurement additionally comprises a means for detecting from the combined spectrum the spectral portion having the highest or lowest frequency and exceeding a predetermined signal power, and a means for deducing the speed from the frequency of the detected spectral portion.

Abstract: A line length measuring device for a fishing reel in which the spool diameter data is obtained on the basis of the time for which an ultrasonic wave is radiated from the ultrasonic sensor mounted on a reel main body onto a spool face of the spool and its reflected wave is received by the ultrasonic sensor, and the line length is measured from the spool diameter data and the number of rotations of the spool detected by rotational number detecting means and displayed. A velocity measuring device is provided for detecting a velocity of the ultrasonic wave radiated from the ultrasonic sensor, in which the spool diameter data is acquired on the basis of the velocity of ultrasonic wave measured by the velocity measuring means.

Abstract: An apparatus (20) determines a vehicle occupant location characteristic. The apparatus (20) includes at least one sensor (e.g., 46) for echo ranging at first and second ultrasonic frequencies. A timer function portion (84) of a microcomputer (66) determines a time-of-flight for each frequency signal. The microcomputer (66) determines the occupant location characteristic using at least one of the determined times-of-flight.

Abstract: A method of tracking an object comprising the steps of acquiring the position of at least one object; selecting the at least one object as a target; determining a sampling window which envelopes the target; obtaining an echo; repeating the foregoing step of obtaining an echo a predetermined number of times; determining valid echoes from the target; calculating the current position of the target from the received echoes; and repeating the steps of obtaining, repeating, determining, and calculating as desired. The step of obtaining an echo comprises the steps of transmitting a pulse at a desired frequency from a transducer; scanning for echoes within the sampling window by a receiver; and receiving at least one echo of the pulse at the receiver which are within the sampling window, the at least one echo having a frequency that matches the outgoing pulse frequency.

Abstract: A vehicle occupant sensor which utilizes an acoustic system for determining object range, extent, and direction. The system is composed of an ultrasonic transmitter formed from an array of air chamber resonator elements driven in relative phase to each other to produce a steered acoustic beam. Electrical excitation circuitry converts waveform data stored in memory elements to electrical signals to drive the transmitter. One or more ultrasonic receivers receives the acoustic waves reflected from objects, and a processor determines the range, extent and direction of the objects based on the received acoustic waves.

Abstract: For use with a high gain receiver circuit which receives echo pulses of frequencies within a predetermined bandwidth and at times within interpulse periods of a predetermined pulse repetition rate and amplifies the echo pulses for measurement purposes, the receiver circuit susceptible to electrical noise within the frequency bandwidth of the received echo pulses to create false echo pulses, a method of eliminating substantially the false echo pulses without affecting substantially the amplified echo pulses by accepting only echo pulses which occur synchronously among interpulse periods. The pulse repetition rate may be varied to eliminate false echo pulses that are synchronous to the interpulse periods.

Abstract: A distance measuring and monitoring device equipped automobile reverse radar comprises: a photocoupler camera with a wide-angle lens installed at an automobile rear end for taking pictures of possible obstacles behind the automobile body; a distance measuring inductor for calculation of lateral distance between two lateral corners of the automobile body and an obstacle; and a power supply for supplying power to the photocoupler camera, the distance measuring inductor, and the display. The image of the obstacle is mirror-image processed, then forwarded to an image synthesizer for image synthesization, and transferred to a video processor and shown in a display. A reverse gear signal is the effective signal for triggering the power supply.

Abstract: A method for determining the velocity of features such as wind. The method preferably includes producing sensor signals and projecting the sensor signals sequentially along lines lying on the surface of a cone. The sensor signals may be in the form of lidar, radar or sonar for example. As the sensor signals are transmitted, the signals contact objects and are backscattered. The backscattered sensor signals are received to determine the location of objects as they pass through the transmission path. The speed and direction the object is moving may be calculated using the backscattered data. The data may be plotted in a two dimensional array with a scan angle on one axis and a scan time on the other axis. The prominent curves that appear in the plot may be analyzed to determine the speed and direction the object is traveling.

Abstract: The invention concerns a temporal and spectral submarine locating method, characterised in that it consists in: equipping the systems or mobile objects to be located and/or identified, with acoustic transmitters transmitting aperiodic signals with a predetermined pseudo-random sequence: deploying, over the working zone where the systems and moving objects to be located are found, one or several measuring points provided, each with an acoustic receiver, with a time scale reference and means for locating said measuring point; transmitting to a processing centre data derived from the measuring points where, at every time of detection on a given frequency band, precise dating is associated in a time scale referential with a position of said measuring point in a spatial referential; the whole set of data derived from the different measuring points being assembled at said processing centre to be operated on by level 2 correlation with the pseudo-random reference sequences corresponding to each of the searched trans

Abstract: A power saving system and method for the analog-to-digital converter stage in a time of flight ranging system. A receiving echo signal having an envelope is converted into a digital form suitable for further processing by sampling the received echo signal envelope at precise intervals to obtain amplitude measurement points. An interpolation function is applied between each pair of adjacent amplitude measurement points. The application of the interpolation function provides a closer approximation of the shape of the received echo signal envelope without the need to use higher sampling rates which means slower analog-to-digital converters may be utilized resulting in power and cost savings.

Abstract: The present invention pertains to a method for range measurement by means of a signal transmitted in the direction of an object to be measured, wherein an echo signal, on which is superimposed a first reference pulse, is received by a receive device, wherein the echo signal is compared with a second reference signal that features a second reference pulse for determining a signal travel time, and wherein a first comparison value of the echo signal and a second comparison value of the second reference signal are compared with each other for determining an amplitude offset between the echo signal and the second reference signal, and these values, in regards to time, are before the first and second reference pulses in a region of the echo signal curve and of the second reference signal curve, respectively, and in these regions, these curves feature a slope that is at least approximately zero.